According to the National Committee on Pay Equity, in 2012, womens’ pay was 77 percent of a man’s pay despite the data showing more women are graduating from college than men and are earning higher grades.

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Give Mr. Ploof some credit: As he has phrased it, the question he raises already contains the germ of the answer. He is aware at some level that if we want to know whether employers are discriminating on the basis of sex, we must compare not simply what all men and women earn on average, but must compare men and women all other things being equal.

So he contemplates controlling for education. He observes that more women graduate from college than men and are earning higher grades.

Why is this? In our survey, women were more likely to say they had taken career interruptions to care for their family. And research has shown that these types of interruptions can have an impact on long-term earnings. Roughly four-in-ten mothers say they have taken a significant amount of time off from work (39%) or reduced their work hours (42%) to care for a child or other family member. Roughly a quarter (27%) say they have quit work altogether to take care of these familial responsibilities. (Fewer men say the same. For example, just 24% of fathers say they have taken a significant amount of time off to care for a child or other family member.)

Even though women have increased their presence in higher-paying jobs traditionally dominated by men, such as professional and managerial positions, women as a whole continue to work in lower-paying occupations than men do.

Don’t think Pew is arguing for my side here—Pew concludes that part of the remaining gap may be due to discrimination.

The problem is that every time we control for more variables, the “gap” changes; some of it is explained by things other than discrimination. It would be arbitrary to stop controlling for variables at some point and assume that the remaining gap is due to discrimination. It would probably also be impossible to control for all the relevant variables. When we talk about a “pay gap”, we are claiming to know something that is not known and is probably unknowable.

A common procedure in trying to prove discrimination with statistics is to (1) establish that there are statistical disparities between two or more groups, (2) demonstrate that the odds that these particular disparities are a result of random chance are very small, and (3) show that, even holding constant various nondiscriminatory factors which might influence the outcomes, that still leaves a substantial residual difference between the groups, which must be presumed to be due to discrimination. Since essentially the same intellectual procedure has been used to “prove” genetic inferiority, the choice of what to attribute the residual to is inherently arbitrary. But there is yet another major objection to this procedure. Not uncommonly, as the gross statistics are broken down by holding various characteristics constant, it turns out that the groups involved differ in these characteristics on every level of aggregation—and differ in different proportions from one level to another.

The residual fallacy is one of the grand non sequiturs of our time, as common in the highest courts of the land as on the political platform or in the media or academe. At the heart of the fallacy is the notion that you really can hold variables constant—“controlling” the variables, as statisticians say—in practice as well as in theory.

“Controlling” for Education

A commonly made claim is that discrimination is so pervasive and so severe that even people with the same educational qualifications are paid very differently according to whether they are male or female, black or white, etc. Holding years of education constant is often illusory, however, since groups with different quanities of education often have qualitative differences in their education as well. Thus, when group A has significantly more years of education than group B, very often group A also has a higher quality of education, whether quality is measured by their own academic performance at a given educational level, by the qualitative rankings of the institutions attended, or by the difficulty and remuneration of the fields of study in which the group is concentrated. At the college or university level, for example, group A may be more heavily concentrated in mathematics, science, medicine, or engineering, while group B is concentrated in sociology, education, or various ethnic studies. In this context, claims that members of group B are paid less than members of group A with the “same” education (measured quantitatively) are clearly fallacious. Qualitative differences in education between groups have been common around the world, whether comparing Asian Americans with Hispanic Americans in the United States, Ashkenazic Jews with Sephardic Jews in Israel, Tamils with Sinhalese in Sri Lanka, Chinese with Malays in Malaysia, or Protestants with Catholics in Northern Ireland.

Male-female differences in income are often likewise said to prove discrimination because men and women with the “same” education receive different pay. Suppose, for example, that we try to hold education constant by examining income statistics just for those women and men who have graduated from college. There is still a sex difference in income at this level of aggregation, and if we are content to stop here—the choice of stopping point being inherently arbitrary—then we may choose to call the residual differences in income evidence of sex discrimination. However, if we recognize that college graduates include people who go on to postgraduate study, and that postgraduate education also influences income, we may wish to go on to the next level of aggregation and compare women and men who did postgraduate study. Now we will find that the proportion of women and men with postgraduate degrees differs from the proportions with college degrees—women slightly outnumbering men at the bachelor’s degree level, but being outnumbered by men by more than two-to-one at the master’s degree level, and by 59 percent at the Ph.D. level. Clearly, when we compare college-educated women and men, which includes those who went on to postgraduate work, we are still comparing apples and oranges because their total education is not the same.

Suppose, then, that we press on to the next level of aggregation in search of comparability, and look only at women and men who went all the way to the Ph.D. Once more, we will discover not only disparities but changing ratios of disparities. Although women receive 37 percent of all Ph.D.s, the fields in which they receive them differ radically from the fields in which men receive their Ph.D.s—with the men being more heavily concentrated in the more mathematical, scientific, and remunerative fields. While women receive nearly half the Ph.D.s in the social sciences and more than half in education, men receive more than 80 percent of the Ph.D.s in the natural sciences and more than 90 percent of the Ph.D.s in engineering. We are still comparing apples and oranges.

Some specialized studies have permitted even finer breakdowns, but sex disparities in education continue in these finer breakdowns as well. For example, if we examine only those women and men who received Ph.D.s in the social sciences, it turns out that the women were more likely to be in sociology and the men in economics—the latter being the more remunerative field. Moreover, even within economics, there have been very large male-female differences as to what proportion of the economics Ph.D.s were specifically in econometrics—a difference in a proportion of ten men to one woman. In short, we have still not held constant the education we set out to hold constant and which we could have said that we had held constant by simply stopping the disaggregation at any point along the way.

While the disaggregation process must stop at some point, whether because the statistics are not broken down any further or because time is not limitless, the fatal fallacy is to assume that all factors left unexamined must be equal, so that all remaining differences in outcome can be attributed to discrimination. In other words, having found causal disparities at every level of aggregation—and often changing ratios of such disparities, as well—it is arbitrarily assumed that the causal disparities end where our disaggregation ends, so that all remaining differences in regard must be due to discrimination.

Innumerable historical and cultural differences, found among many groups in countries around the world—as the numbered examples listed above [buy the book] suggest—make statistical disparities fall far short of proof of discrimination. Such data may be accepted as evidence or proof in courts of law but, logically speaking, such data prove nothing. They are “Aha!” statistics.

(End notes with sources omitted. Emphasis in original. List of interesting examples of group disparities from world history omitted.)

Anyway as commenter Jack Curtis points out, what’s the alternative? that women are just as good workers as men, and men cost about a third more, and employers aren’t hiring women in droves? The same labor but 23% cheaper—that’s quite a bargain, and if there’s one thing businesses love, it’s cutting costs. (OK, maybe if there’s one thing businesses love, it’s making money, but if there are two things businesses love, they’re making money and cutting costs.) Under these circumstances, why would employers be hiring any men?

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The public-policy history perhaps similarly proves too much. In the 2012 presidential debates, President Obama in effect wanted to take credit for making it against the law for employers to discriminate on the basis of sex. Again, give Mr. Ploof some credit: He notes that it has already been against the law nationwide since 1963; the 2009 Lilly Ledbetter Act makes comparatively minor adjustments, such as lengthening the statute of limitations on discrimination lawsuits.

Now Mr. Ploof, Democrats in the Senate, and President Obama want a third law, the Paycheck Fairness Act. Well, which is it? Can President Obama claim victory for the Lilly Ledbetter Act, or are knuckle-dragging employers still paying men a third more than women, doggedly still swimming fiercely upstream against the law, the culture, and their own economic interests? The Democrats can’t just keep raising the issue as a punching bag and declaring victory over it every couple of years.

(3)

There’s also the inconvenient fact that if we judge them by the same (clearly wrong, bad epistemology) standards, the Democrats who call for these laws are themselves “discriminating against women” the same as everyone else, which again suggests that the issue is a useful political punching bag for them rather than a real issue that needs to be addressed. Or, as even the liberal Washington Post put it just a couple of months ago, “Male-female pay gap remains entrenched at White House”:

The average male White House employee currently earns about $88,600, while the average female White House employee earns about $78,400, according to White House data released Tuesday. That is a gap of 13 percent.

In 2009, male employees made an average of about $82,000, compared to an average of $72,700 earned by female employees — also a 13 percent wage gap.

Wait, the Obama administration says, we can explain!

White House officials say that even if the aggregate statistics show a gap, men and women in the same roles at the White House are paid similar amounts. “At the White House, we have equal pay for equal work,” said White House spokeswoman Jessica Santillo. “Men and women in equivalent roles earn equivalent salaries . . . .”

Right. If there’s an apparent pay gap in the punching-bag private sector, it must be due to discrimination. If there’s an apparent pay gap in Democrats’ employ, it must be that we’re not comparing apples to oranges.

[…] without qualification, “Women continue to be paid less than men for the same work,” which we know either isn’t true or isn’t known—but even he is struck by the implicit tension between different “waves” of […]